Recently, with improvement in fine pattern processing technologies in semiconductor and other industries, small deviations from design values of the pattern become problems. Especially, degradation in a two-dimensional form and dimensional variation that are noticeable even by top-down observation cause large influence in device performance. Then, there has arisen a need to measure and evaluate edge roughness and amount of CD variation (CD uniformity across a wafer top surface, CD variation among wafers, etc.) more correctly. For example, edge roughness occurred in the gate of a transistor causes, first, a local short channel effect. Therefore, even if the average gate length in the transistor has such a value as a design specifies, transistor performance gets worse than a design value. Second, the average gate length in the transistor itself deviates from the design value.
Recently, influence of edge roughness described above, especially edge roughness on a line pattern (line-edge roughness), on transistor performance has started to be discussed actively, as described in, for example, Non-patent literatures 1 to 7. As a result, a problem of measurement of line-edge roughness in addition to the conventional dimensional measurement has arisen also in measurement equipment. Generally, a difference between a maximum value and minimum value obtained by statistically processing roughness data (sequence data) that are obtained by measuring edge points of a line pattern or line widths at constant intervals, three times the standard deviation of its distribution, or the like is used as an index of line-edge roughness. However, determination using one kind of index out of these indexes has two problems. First, this determination cannot compare data of different sampling conditions. This is because an index value depends largely on sampling conditions of the data (a dimension of measurement area used to compute a degree of roughness and a sampling interval at which edge points are extracted) as described in Non-patent document 7. For example, in the case where two kinds of patterns A and B are measured with respective different observation magnifications, it is very difficult to equalize a detection interval of edge-points used to calculate line-edge roughness and a measurement area for two kinds of images, because the length and resolution for one pixel are different.
For this reason, regarding the degree of roughness, it is often the case that discussion is given up and the roughness is measured again. Such a problem is likely to occur in a research and development phase. Second, a spatial period of roughness cannot be expressed with one kind of index. For example, in the case of the line-edge roughness on the gate described at the beginning, the roughness that produces a local short channel effect described as the first example is of a comparatively short period. On the other hand, this roughness that produces a shift in the average gate length described in the second example is of a long period. In a process of making transistors of short gate widths, roughness of a long period becomes comparatively large. Therefore, although the performance of individual transistors does not degrade, performance variation as a whole becomes large. On the other hand, in a manufacturing process of transistors of long gate widths, performance variation is small, but a short channel effect is easy to occur for every transistor.
In order to realize high productivity in a semiconductor mass-production system, it is necessary to perform evaluation suitable for properties of a product and its transistor structure. For that purpose, an index containing characteristics of spatial frequency becomes necessary besides only measuring a degree of line-edge roughness always under constant measurement conditions.
What is necessary to indicate characteristics of spatial periods of line-edge roughness is to Fourier transform roughness data obtained by measuring edge points of a line pattern or line widths at constant intervals and display its Fourier spectrum (amplitude spectrum or power spectrum). This is for solving the second problem described above, but at the same time can solve the first problem. By comparing the magnitude of each frequency component of the Fourier spectrum, the magnitude relation of roughness can be determined regardless of measurement conditions of the roughness data.
In research and development, these techniques are employed. As described in Non-patent literatures 7 to 9, there are examples of actual reports. However, it is difficult to grasp instantaneously characteristics of the line-edge roughness related to the frequency distribution visually from these spectra on which noises have a large influence. It takes a time to compare and examine Fourier spectra having a lot of noises visually and involves a possibility that different results are obtained depending on a viewer. So, an index that simply represents the characteristics of a frequency distribution becomes necessary. Especially in an inspection process in volume production, the need is larger.
Moreover, the conventional CD measurement is not predicated the existence of line-edge roughness. For example, in the presence of line-edge roughness, CD may vary depending on which position is measured on the line. Because of this, measured values of CD uniformity across a wafer plane and amount of variation among wafers depend on line-edge roughness occurring at random, and consequently it becomes impossible to measure CD variation resulting from variation in anneal temperature and variation in an underlayer thickness. For the method of CD measurement, a countermeasure is becoming necessary.
Note that a term, line-edge roughness is a term indicating a variation in edge positions of a line pattern. However, it is often the case that this term is used for both a variation in edge positions and a variation in line widths along the line. Hereafter, as a term especially for a variation in edge positions, an expression of the line-edge roughness in the narrow sense will be used. Moreover, an expression of line width roughness will be used for a variation in line width along the line.
[Non-patent document 1]    Digest of SISPAD 2000 (2000), pp. 131-134
[Non-patent document 2]    IEDM Technical Digest 2000 (2000), pp. 563-567
[Non-patent document 3]    IEEE Electron Device Letters, Vol. 22 (2001), pp. 287-289
[Non-patent document 4]    Proc. SPIE 4689 (2002), pp. 733-741
[Non-patent document 5]    IEDM Technical Digest 2002 (2002), pp. 303-306
[Non-patent document 6]    IEDM Technical Digest 2002 (2002), pp. 307-310    [Non-patent document 7]    Proc. SPIE 5038 (2003), pp. 689-696